Browsing by Author "Erni, Birgit"

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    Open Access
    Analysis of distribution maps from bird atlas data: dissimilarities between species, continuity within ranges and smoothing of distribution maps
    (1998) Erni, Birgit; Underhill, Les
    A dissimilarity coefficient for estimating the dissimilarity between two bird atlas distributions is developed. This coefficient is based on the Euclidean distance concept. The atlas distributions are compared over all quarter degree grid cells. Existing coefficients are not suitable for the comparison of distributions with different total areas and species with different mean reporting rates. In each grid cell the reliability of the reporting rates depends on the number of checklists collected for the grid cell. Weights are used to solve this problem. To solve the problem of different levels of abundance and conspicuousness of species, the reporting rates are sorted into percentiles, using five or 10 categories for the strictly positive reporting rates. Each grid cell is weighted by a function of the number of checklists collected for the grid cell. The coefficient is scaled by the maximum possible sum of the differences which would occur if there is no overlap between the two distributions, so that the dissimilarity coefficient lies between zero (a perfect match) and one (no overlap). A variety of these coefficients are investigated and compared. The continuity of observed reporting rates in a spatial cellular map is an indication of spatial autocorrelation present, especially between observations which are in close vicinity. We are particularly interested in measuring and comparing the continuity of the reporting rates in the bird distributions from The Atlas of Southern African Birds. The variogram, developed in geostatistics, estimates this spatial autocorrelation. The classical variogram estimator, however, is dependent on the scale of measurement and assumes that the data are intrinsically stationary. The bird atlas distribution maps contain trend and the variance of each observation (reporting rate) is a function of the number of checklists collected for the grid cell and the underlying probability of encountering the species in the grid cell. The approach of removing this binomial measurement error from the variogram developed by McNeill (1991) is investigated but not found satisfactory. A weighted variogram, where each squared difference is weighted by a function of the smaller number of checklists, is developed. To make the variogram values comparable between species a function of the mean reporting rates is used to scale the variogram. We were particularly interested in the first variogram value of each species distribution, 2y(1). The bird distribution maps in The Atlas of Southern African Birds show the raw observed reporting rates. Each of these reporting rates is a random variable dependent on sampling error due to binomial variation based on the number of checklists collected for the grid cell and on the underlying probability of encountering the species. The distribution maps show this measurement error. It is believed that a smoothed version of the bird distribution maps will to some extent improve the statement these observed distributions are aiming to make. Single-step regression methods are investigated for a fast approach to this problem. These cause problems because of frequent 'zero' observed reporting rates and because they smooth the maps too heavily. Generalized Linear Models are investigated and this iterative procedure is applied to model the reporting rates with a binomial distribution on square blocks of nine grid cells where a value for the central cell is 'predicted' in each regression. This approach is especially suited to accommodate the binomial distribution characteristics and is found to smooth the bird atlas distributions well. Because only a local window is taken for each regression, the spatial autocorrelation is adequately included in the spatial explanatory variables.
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    Bayesian analysis of historical functional linear models with application to air pollution forecasting
    (2022) Junglee, Yovna; Erni, Birgit; Clark, Allan
    Historical functional linear models are used to analyse the relationship between a functional response and a functional predictor whereby only the past of the predictor process can affect the current outcome. In this work, we develop a Bayesian framework for the analysis of the historical functional linear model with multiple predictors. Different from existing Bayesian approaches to historical functional linear models, our proposed methodology is able to handle multiple functional covariates with measurement error and sparseness. The proposed model utilises the well-established connection between non-parametric smoothing and Bayesian methods to reduce sensitivity to the number of basis functions which are used to model the functional regression coefficients. We investigate two methods of estimation within the Bayesian framework. We first propose to smooth the functional predictors independently from the regression model in a two-stage analysis, and secondly, jointly with the regression model. The efficiency of the MCMC algorithms is increased by implementing a Cholesky decomposition to sample from high-dimensional Gaussian distributions and by taking advantage of the orthogonal properties of the functional principal components used to model the functional covariates. Our extensive simulation study shows substantial improvements in both the recovery of the functional regression surface and the true underlying functional response with higher coverage probabilities, when compared to a classical model under which the measurement error is unaccounted for. We further found that the Bayesian two-stage analysis outperforms the joint model under certain conditions. A major challenge with the collection of environmental data is that they are prone to measurement error, both random and systematic. Hence, our methodology provides a reliable functional data analytic framework for modelling environmental data. Our focus is on the application of our method to forecast the level of daily atmospheric pollutants using meteorological information such as hourly records of temperature, humidity and wind speed from data collected by the City of Cape Town, South Africa. The forecasts provided by the proposed Bayesian two-stage model are highly competitive against the functional autoregressive models which are traditionally used for functional time series.
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    Changes in rainfall seasonality in the Western Cape, South Africa: an exploration of methods for determining the start and end of the rainfall season
    (2020) Ivey, Peter; Erni, Birgit
    The aim of this thesis is to detect and analyse changes in seasonality in rainfall for various groups of weather stations in the Western Cape area. Weather stations with similar seasonal patterns are firstly grouped together using certain clustering algorithms. The start and end of the rainfall season dates for the different groups of weather stations are estimated and then compared over time to determine whether there have been any changes. Once these start and end of season dates have been estimated, the length of the rainfall season is estimated and compared over time. Studies have been performed globally and over southern Africa attempting to analyse rainfall patterns and changes. However, rainfall is the most unstable climate variable in terms of time and space and thus, it is really difficult to predict (Yaman, 2018). Most studies have pointed toward an increase of extreme events on both sides of the scale i.e. more intense flooding and more severe drought being experienced. Some places are also starting to experience more rainfall than before whilst other places are starting to experience more drought. The impacts of these rainfall changes are already being experienced with many areas being forced to adapt to the new conditions. Many better decisions can be made with a better understanding of how rainfall seasons are changing. In the agricultural industry, better informed decisions about when the rainfall season is likely to start and end can result in more optimal yield from crops. Changes in rainfall can also affect the type of crops that should be planted. Farmers will also be able to better prepare for drought seasons if they are better informed as to when these drought periods will likely occur. In terms of disaster risk management, the more that is known about rainfall patterns, the better prepared regions can be for the inevitable increase in extreme events. Cities can put in better systems now in order to deal with potential future crises. Cape Town is an example of a city that could have possibly been better prepared for the current drought crisis if there was a better understanding of rainfall trends. Hopefully in the future, with more accurate information about rainfall, it can rather be an active process than a reactionary process to the current climate conditions.
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    Citizen science reveals complex changes in barn swallow phenology in South Africa over three decades
    (2016) Burman, Marc Sebastian; Underhill, Leslie G; Altwegg, Res; Erni, Birgit; Remisiewicz, Magdalena
    Palearctic migrants, including barn swallows Hirundo rustica, responded to climate change in Europe from the mid to late 1900s with phenological changes, mostly showing earlier arrival and start of breeding. During this period, barn swallows in the Palearctic exhibited variable patterns of change in the timing of their arrival, breeding and departure from the breeding grounds. At the South African non-breeding grounds, the timing of migration shifted between the 1980s and 2000s, again with geographic variability. To explain these changes further, I examined geographic and temporal variability in the timing of flight feather ('primary') moult, and trends in body weight, in barn swallows ringed in South Africa between 1986 and 2012. Citizen science bird ringing, started in South Africa in 1948, generated all the data used in this project. All data were obtained from the South African Bird Ringing Unit (SAFRING).
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    A continuous-time formulation for spatial capture-recapture models
    (2016) Distiller, Greg; Borchers, David; Erni, Birgit
    Spatial capture-recapture (SCR) models are relatively new but have become the standard approach used to estimate animal density from capture-recapture data. It has in the past been impractical to obtain sufficient data for analysis on species that are very difficult to capture such as elusive carnivores that occur at low density and range very widely. Advances in technology have led to alternative ways to virtually "capture" individuals without having to physically hold them. Some examples of these new non-invasive sampling methods include scat or hair collection for genetic analysis, acoustic detection and camera trapping. In traditional capture-recapture (CR) and SCR studies populations are sampled at discrete points in time leading to clear and well defined occasions whereas the new detector types mentioned above sample populations continuously in time. Re- searchers with data collected continuously currently need to define an appropriate occasion and aggregate their data accordingly thereby imposing an artificial construct on their data for analytical convenience. This research develops a continuous-time (CT) framework for SCR models by treating detections as a temporal non homogeneous Poisson process (NHPP) and replacing the usual SCR detection function with a continuous detection hazard func- tion. The general CT likelihood is first developed for data from passive (also called "proximity") detectors like camera traps that do not physically hold individuals. The likelihood is then modified to produce a likelihood for single-catch traps (traps that are taken out of action by capturing an animal) that has proven difficult to develop with a discrete-occasion approach. The lack of a suitable single-catch trap likelihood has led to researchers using a discrete-time (DT) multi-catch trap estimator to analyse single-catch trap data. Previous work has found the DT multi-catch estimator to be robust despite the fact that it is known to be based on the wrong model for single-catch traps (it assumes that the traps continue operating after catching an individual). Simulation studies in this work confirm that the multi-catch estimator is robust for estimating density when density is constant or does not vary much in space. However, there are scenarios with non-constant density surfaces when the multi-catch estimator is not able to correctly identify regions of high density. Furthermore, the multi-catch estimator is known to be negatively biased for the intercept parameter of SCR detection functions and there may be interest in the detection function in its own right. On the other hand the CT single-catch estimator is unbiased or nearly so for all parameters of interest including those in the detection function and those in the model for density. When one assumes that the detection hazard is constant through time there is no impact of ignoring capture times and using only the detection frequencies. This is of course a special case and in reality detection hazards will tend to vary in time. However when one assumes that the effects of time and distance in the time-varying hazard are independent, then similarly there is no information in the capture times about density and detection function parameters. The work here uses a detection hazard that assumes independence between time and distance. Different forms for the detection hazard are explored with the most exible choice being that of a cyclic regression spline. Extensive simulation studies suggest as expected that a DT proximity estimator is unbiased for the estimation of density even when the detection hazard varies though time. However there are indirect benefits of incorporating capture times because doing so will lead to a better fitting detection component of the model, and this can prevent unexplained variation being erroneously attributed to the wrong covariate. The analysis of two real datasets supports this assertion because the models with the best fitting detection hazard have different effects to the other models. In addition, modelling the detection process in continuous-time leads to a more parsimonious approach compared to using DT models when the detection hazard varies in time. The underlying process is occurring in continuous-time and so using CT models allows inferences to be drawn about the underlying process, for example the time- varying detection hazard can be viewed as a proxy for animal activity. The CT formulation is able to model the underlying detection hazard accurately and provides a formal modelling framework to explore different hypotheses about activity patterns. There is scope to integrate the CT models developed here with models for space usage and landscape connectivity to explore these processes on a finer temporal scale. SCR models are experiencing a rapid growth in both application and method development. The data generating process occurs in CT and hence a CT modelling approach is a natural fit and opens up several opportunities that are not possible with a DT formulation. The work here makes a contribution by developing and exploring the utility of such a CT SCR formulation.
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    The ecology of Namibian fairy circles and the potential role of sand termites (Psammotermes allocerus Silvestri) in their origin
    (2016) Vlieghe, Kelly E P; Picker, Michael D; Erni, Birgit
    Regularly-dispersed patterning in the landscape occurs globally, both in the form of vegetated patches or gaps of bare earth within a vegetated matrix. Most theories link these periodic patterns to various biotic factors including selective grazing, allelopathy, nests of social insects, and competitive interactions between plants ('self-organisation'). Fairy circles are perhaps the most archetypal of these patterns, taking the form of evenly-spaced, circular to elliptical barren patches 2-12m in diameter. They occur in dense fields within sandy, species-poor grasslands in the Pro-Namib Desert. Fairy circles often display a well-vegetated peripheral ring of grasses and have been shown to retain higher levels of soil moisture compared to the surrounding matrix soils. They can persist in the landscape for decades, and show evidence of birth and senescence, when the bare disc becomes overgrown by grasses and fades back into the matrix. Since the 1970's several hypotheses have been forwarded for their origin including; herbivory by the termite Hodotermes mossambicus (or the release of volatile chemicals from their nests), the excavation of grass roots by a widespread and common ant species, an allelopathic chemical released by Euphorbia damarana plants, geochemical gas seeps, plant self-organisation, and nest building activities of the Sand termite Psammotermes allocerus. A consensus has yet to be reached regarding the origin and nature of fairy circles, and the two theories currently receiving the most attention and debate are the Sand termite hypothesis and plant competition hypothesis. The latter proposes that short-range facilitation of plant growth occurs within the matrix and on the periphery of fairy circles, while long-range competition for resources (primarily water) by Stipagrostis roots inhibits plant growth on the bare disc thus generating the regular bare patches. The Sand termite hypothesis states that the termite P. allocerus creates and maintains a bare patch around their polycalic nests primarily through central-based foraging on grass roots and culms. This thesis aims to test the Sand termite hypothesis for fairy circle formation as well as expand on the ecology of fairy circles. Novel features relating to their ecology which are examined include: (1) various potential mechanisms for maintaining the circle's bare appearance (specifically examining seed banks and excavation of seedlings by ants), (2) changes in circle density and size in relation to environmental variables at a local scale (including soil properties and vegetation cover/type), (3) their ontogeny, lifespan and survival, (4) the high degree of spatial ordering seen in fairy circles, (5) soil properties on fairy circles compared to the surrounding matrix (including particle size, temperature, moisture, pH and electrical conductivity) and (6) the influence of fairy circles on nearby plant and insect communities. Fieldwork for the above was carried out in NamibRand Nature Reserve, Southwest Namibia.
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    Modelling growth patterns of bird species using non-linear mixed effects models
    (2008) Ntirampeba, D; Little, Francesca; Erni, Birgit
    The analysis of growth data is important as it allows us to assess how fast things grow and determine various factors that have impact on their growth. In the current study, growth measurements on body features (body mass, wing length, head length, bill (culmen) length, foot length, and tarsus length) for Grey-headed Gulls populating Bonaero Park and Modderfontein Pan in Gauteng province, South Africa, and for Swift Terns on Robben Island were taken. Different methods such as polynomial regressions, non-parametric models and non-linear mixed effects models have been used to fit models to growth data. In recent years, non-linear mixed effects models have become an important tool for growth models. We have fitted univariate inverse exponential, Gompertz, logistic, and Richards non-linear mixed effects models to each of the six body features. We have modeled these six features simultaneously by adding a categorical covariate, which distinguishes between different features, to the model. This approach allows for straightforward comparison of growth between the different body features. In growth studies, the knowledge of the age of each individual is an essential information for growth analysis. For Swift Terns, the exact age of most chicks was unknown, but a small portion of the sample was followed from nestling up to the end of the study period. For chicks with unknown age, we estimated age by fitting the growth curve, obtained from birds with known age, to the mass measurements of the chick with unknown age. It was found that the logistic models were most appropriate to describe the growth of body mass and wing length while the Gompertz models provided best fits for bill, tarsus, head and foot for Grey-headed Gulls. For Swift Terns, the inverse exponential model provided the best univariate fit for four of six features. The logistic model, with a variance function increasing as a power of fitted values, with a different power for each feature and autoregressive correlation structure for within bird errors with errors from different features within the same subject assumed to be independent, gave the best model to describe the growth of all body features taken simultaneously for both Grey-headed Gull and Swift Tern data. It was shown that growth of Grey-headed Gull and Swift Tern chicks occurs in the following order (foot, body mass, tarsus)-(bill, head)-( wing) and (tarsus, foot)-(body mass, bill, head)-(wing) , respectively.
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    Regional COâ‚‚ flux estimates for South Africa through inverse modelling
    (2018) Nickless, Alecia; Rayner, Peter; Scholes, Bob; Erni, Birgit; Underhill, Leslie G
    Bayesian inverse modelling provides a top-down technique of verifying emissions and uptake of carbon dioxide (CO₂) from both natural and anthropogenic sources. It relies on accurate measurements of CO₂ concentrations at appropriately placed sites and "best-guess" initial estimates of the biogenic and anthropogenic emissions, together with uncertainty estimates. The Bayesian framework improves current estimates of CO₂ fluxes based on independent measurements of CO₂ concentrations while being constrained by the initial estimates of these fluxes. Monitoring, reporting and verification (MRV) is critical for establishing whether emission reducing activities to mitigate the effects of climate change are being effective, and the Bayesian inverse modelling approach of correcting CO₂ flux estimates provides one of the tools regulators and researchers can use to refine these emission estimates. South Africa is known to be the largest emitter of CO₂ on the African continent. The first major objective of this research project was to carry out such an optimal network design for South Africa. This study used fossil fuel emission estimates from a satellite product based on observations of night-time lights and locations of power stations (Fossil Fuel Data Assimilations System (FFDAS)), and biogenic productivity estimates from a carbon assessment carried out for South Africa to provide the initial CO₂ flux estimates and their uncertainties. Sensitivity analyses considered changes to the covariance matrix and spatial scale of the inversion, as well as different optimisation algorithms, to assess the impact of these specifications on the optimal network solution. This question was addressed in Chapters 2 and 3. The second major objective of this project was to use the Bayesian inverse modelling approach to obtain estimates of CO₂ fluxes over Cape Town and surrounding area. I collected measurements of atmospheric CO₂ concentrations from March 2012 until July 2013 at Robben Island and Hangklip lighthouses. CABLE (Community Atmosphere Biosphere Land Exchange), a land-atmosphere exchange model, provided the biogenic estimates of CO₂ fluxes and their uncertainties. Fossil fuel estimates and uncertainties were obtained by means of an inventory analysis for Cape Town. As an inventory analysis was not available for Cape Town, this exercise formed an additional objective of the project, presented in Chapter 4. A spatially and temporally explicit, high resolution surface of fossil fuel emission estimates was derived from road vehicle, aviation and shipping vessel count data, population census data, and industrial fuel use statistics, making use of well-established emission factors. The city-scale inversion for Cape Town solved for weekly fluxes of CO₂ emissions on a 1 km × 1 km grid, keeping fossil fuel and biogenic emissions as separate sources. I present these results for the Cape Town inversion under the proposed best available configuration of the Bayesian inversion framework in Chapter 5. Due to the large number of CO₂ sources at this spatial and temporal resolution, the reference inversion solved for weekly fluxes in blocks of four weeks at a time. As the uncertainties around the biogenic flux estimates were large, the inversion corrected the prior fluxes predominantly through changes to the biogenic fluxes. I demonstrated the benefit of using a control vector with separate terms for fossil fuel and biogenic flux components. Sensitivity analyses, solving for average weekly fluxes within a monthly inversion, as well as solving for separate weekly fluxes (i.e. solving in one week blocks) were considered. Sensitivity analyses were performed which focused on how changes to the prior information and prior uncertainty estimates and the error correlations of the fluxes would impact on the Bayesian inversion solution. The sensitivity tests are presented in Chapter 6. These sensitivity analyses indicated that refining the estimates of biogenic fluxes and reducing their uncertainties, as well as taking advantage of spatial correlation between areas of homogeneous biota would lead to the greatest improvement in the accuracy and precision of the posterior fluxes from the Cape Town metropolitan area.
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    Structural time series modelling for 18 years of Kapenta fishing in Lake Kariba
    (2012) Dalmeyer, Lara; Erni, Birgit; Haines, Linda
    Includes abstract. Includes bibliographical references.
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    Using movement modelling to improve the design and analysis of vantage point surveys in bird and wind energy studies
    (University of Cape Town, 2020) Cervantes Peralta, Francisco; Erni, Birgit; Theoni Photopoulou, Theoni; Simmons, Rob
    Wind energy, although mostly a clean and increasingly efficient energy source, is known to affect communities of flying vertebrates. Mortality by collision with turbines is one of the main impacts on birds and bats associated with wind energy. Soaring birds are particularly vulnerable due to their collision prone behaviours, low manoeuvrability, and their slow population recovery rates. The focus of this thesis is on the identification of areas that are intensively used by soaring birds in order to inform wind turbine placement and minimize collision risk. This thesis is particularly concerned with predictions of bird-use intensity that are based on flight trajectories mapped by observers from vantage points. This survey technique is standard practice during the environmental impact assessment of wind energy facilities, although its virtues and limitations are largely untested. Flight trajectories are counted, timed and mapped during these surveys. However, most assessments ignore the spatial information contained in the trajectories, and mappings are often reduced to metrics such as closest distance to a turbine or whether a particular habitat is visited. In this thesis, I use visual mappings of flight trajectories to estimate the long-term distribution of bird activity using: i) a kernel density estimator adapted to calculate the density of flight trajectories, and ii) modelling flights as being driven by a stochastic process under the influence of a potential field. Acknowledging the subjectivity introduced in the mapping of trajectories by field observers, I also study the discrepancy between mapped and true trajectories. Finally, I showcase the application of the various analytical techniques with a case study, in which I compare collision risk predictions with actual observed fatalities at a wind farm in South Africa. Kernel density estimation proved to be a good exploratory technique, and the estimator designed to estimate trajectory density outperformed other methods that ignore the temporal structure in trajectory data. Nevertheless, kernel methods are limited by its inability to predict bird activity outside areas observed from vantage points. Potential-based models allowed predictions in unobserved areas based on landscape characteristics, and showed promising results identifying areas of high collision risk. I found that the difference between true and mapped trajectories can be substantial, and it should be accounted for in any spatial analysis of vantage point observations. Although based on a single study case, the results are promising and show that the spatial distribution of collision risk predicted with the suite of methods presented in this thesis correlates well with the distribution of observed fatalities. The framework proposed to predict collision risk improves existing procedures in that it uses movement and spatial information contained in the observed trajectories. In addition, it accounts for all known sources of uncertainty throughout the modelling process.
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    Using state-space time series analysis on wetland bird species to formulate effective bioindicators in the Barberspan wetland
    (2022) Edwards, Gareth; Altwegg, Andreas; Erni, Birgit
    The Coordinated Waterbird Count dataset (CWAC) is a dataset containing waterbird counts from wetlands across South Africa, going as far back as 1970. These data contain valuable information on population sizes and their trends over time. This information could be used more widely if it was more easily accessible to users. The aim of this dissertation is to bridge the gap between the CWAC dataset and the end users (for both experts and non-experts). In so doing the report also provides valuable insight into the state of wetlands in South Africa using various biodiversity indices, starting with Barberspan wetland as the pilot study site. A state-space time series model was applied to the waterbird counts in the CWAC dataset to determine waterbird population trends over the years. Statespace models are able to separate observation error from true population process error, thus providing a more accurate estimation of true population size. This qualifies state-space models as an ideal tool for population dynamics. The state-space model produced estimates of true population size for each waterbird per year. Three different indices were applied to the estimates, namely, exponentiated Shannon's index, Simpson's index and a modified Living Planet Index. These indices aggregate the count data to a measure of effective number of waterbirds in an ecosystem, a measure of evenness of an ecosystem, and an abundance index respectively. Using these three indices, in conjunction with each other, and individual waterbird species as bioindicators for various wetland traits, the end user is presented with a broad overview of the state of the Barberspan wetland. The implication of this research is beneficial to various wetland conservation organisations globally (AEWA, Aichi, RAMSAR) and locally (Working for Wetlands), as it provides valuable insight into the state of wetlands of South Africa. Furthermore, it helps managers at a local level in their decision making to enable more evidence-based approaches to protect South African wetlands and its waterbirds.